Turbine bucket with endwall contour and airfoil profile

ABSTRACT

Turbine frequency tuning, fluid dynamic efficiency, and performance can be improved using an airfoil profile and/or an endwall contour including at least one of a pressure side bump, a pressure side leading edge bump, or a suction side trough. In particular, by including two endwall bumps on the pressure side and a trough on the suction side combined with a particular airfoil profile, performance can be further improved.

BACKGROUND OF THE INVENTION

The subject matter disclosed herein relates to turbine components foraircraft and power generation applications, and, more specifically, toturbine buckets including a base with an endwall contour, and an airfoilportion having a profile that can enhance performance.

Some aircraft and/or power plant systems, for example certain jetaircraft, nuclear, simple cycle and combined cycle power plant systems,employ turbines in their design and operation. Some of these turbinesinclude one or more stages of buckets which during operation are exposedto fluid flows. Each bucket can include a base supporting a respectiveairfoil (e.g., turbine blade, blade, etc.) configured to aerodynamicallyinteract with and extract work from fluid flow (e.g., creating thrust,driving machinery, converting thermal energy to mechanical energy, etc.)as part of, for example, power generation. As a result of thisinteraction and conversion, the aerodynamic characteristics and lossesof these airfoils have an impact on system and turbine operation,performance, thrust, efficiency, and power at each stage.

BRIEF DESCRIPTION OF THE INVENTION

A first embodiment of the invention disclosed herein can include aturbomachine bucket having a base and an airfoil supported by the base.The airfoil can include opposed first and second ends with the first endat the base, as well as opposed pressure and suction sidewalls thatextend in chord between opposed leading and trailing edges and thatextend in span between the first and second ends of the airfoil. Anendwall of the base can be connected to the first end of the airfoil andcan include opposed endwall leading and trailing edges that extendsubstantially circumferentially between opposed pressure and suctionsplitlines, a distance between the pressure and suction splitlines beingsubstantially equal to a pitch. Opposed leading edge and trailing edgeregions of the endwall can each extend from the respective endwallleading and trailing edges to about half way therebetween, and pressureside and suction side regions of the endwall can extend from therespective pressure and suction sidewalls of the airfoil. At least onepressure side feature can be included in the endwall in the pressureside region, each respective pressure side feature including at leastone of a trough or a bump relative to a nominal surface of the endwall.In addition, at least one suction side feature can be included in theendwall in the suction side region, each respective suction side featureincluding at least one of a trough or a bump relative to the nominalsurface of the endwall. At least one leading edge feature can also beincluded in the endwall including at least one of a trough or a bumprelative to the nominal surface in the leading edge region.

In addition, a second embodiment of the invention disclosed herein canbe implemented as an endwall of a flow passage formed by adjacent firstand second substantially identical, substantially circumferentiallyspaced apart airfoils of adjacent buckets of a stage of a turbomachine,a spacing between adjacent airfoils being a pitch. Each airfoil caninclude respective opposed pressure and suction sidewalls extendingchordwise between opposed leading and trailing edges and extendingspanwise between opposed first and second ends. The endwall can includea nominal surface between opposed endwall leading and trailing edges,and can also include a region between the pressure sidewall of the firstairfoil and the suction sidewall of the second airfoil. The endwall canfurther have at least one pressure side feature including at least onebump relative to the nominal surface proximate the pressure sidewall ofthe first blade, as well as at least one suction side feature includingat least one trough relative to the nominal surface.

Further, a third embodiment of the invention disclosed herein can takethe form of a turbine system including a compressor section, acombustion section, and a turbine section. The turbine section caninclude at least one stage of airfoils substantially circumferentiallydistributed at a pitch about an axis of rotation of the turbine section.Each airfoil can be supported by a respective platform of a respectivebucket such that adjacent airfoils form a flow passage including apressure sidewall of a first airfoil, a suction sidewall of a second,adjacent airfoil, and an endwall formed by at least a portion of each ofthe respective platforms of the first and second airfoils. At least oneof the suction sidewall or the pressure sidewall can include a nominalprofile substantially in accordance with non-dimensional Cartesiancoordinate values of X, Y, and Z set forth in TABLE I, wherein thecoordinate values are non-dimensionalized and convertible to distancesby multiplying the coordinate values by a desired span in units ofdistance, and wherein X and Y values connected by smooth continuing arcsdefine profile sections of the at least one of the suction sidewall orthe pressure sidewall at each distance Z along the airfoil, the profilesections at the Z distances being joined smoothly with one another toform the profile of the at least one of the suction sidewall or thepressure sidewall.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of this invention will be more readilyunderstood from the following detailed description of the variousaspects of the invention taken in conjunction with the accompanyingdrawings that depict various embodiments of the invention, in which:

FIG. 1 shows a three-dimensional partial cut-away perspective view of aportion of a turbine according to an embodiment of the invention;

FIG. 2 shows a portion of a set of buckets according to embodiments ofthe invention disclosed herein.

FIG. 3 shows a cross sectional view of a pair of the buckets accordingto embodiments of the invention disclosed herein and shown in FIG. 2taken along corresponding sections 271.

FIG. 4 shows a perspective view of a turbine bucket according toembodiments of the invention disclosed herein.

FIG. 5 shows a schematic block diagram illustrating portions of acombined cycle power plant system in which embodiments of the inventiondisclosed herein can be used.

FIG. 6 shows a schematic block diagram illustrating portions of asingle-shaft combined cycle power plant system in which embodiments ofthe invention disclosed herein can be used.

It is noted that the drawings of the invention are not necessarily toscale. The drawings are intended to depict only typical aspects of theinvention, and therefore should not be considered as limiting the scopeof the invention. It is understood that elements similarly numberedbetween the FIGURES may be substantially similar as described withreference to one another. Further, in embodiments shown and describedwith reference to FIGS. 1-6, like numbering may represent like elements.Redundant explanation of these elements has been omitted for clarity.Finally, it is understood that the components of FIGS. 1-6 and theiraccompanying descriptions may be applied to any embodiment describedherein.

DETAILED DESCRIPTION OF THE INVENTION

Aspects of the invention provide for a turbine bucket including improvedfeatures, such as a base with an endwall contour, an airfoil including aparticular profile and/or a fillet on an end of the airfoil, and/or acooling passage including a tipturn at a tip of the airfoil. To bettermeet system requirements and/or design goals, overall efficiency andairfoil loading capability can be improved by, for example, using animproved endwall contour, airfoil profile, and/or cooling passage designaccording to embodiments of the invention disclosed herein. In addition,thermal and mechanical operating requirements for a given stage can bemet, component lifetime can be improved, cost can be lowered, and/or anyother suitable system requirement and/or design goal can be improved.

Further, aspects of the invention can include a turbine bucket with abase supporting an airfoil at a first end of the airfoil. A top portionof the base at the first end of the airfoil can be construed as aplatform or as an endwall. In contrast to conventional approaches, theendwall can include a non-axisymmetric contour that can enhance fluidflow over the endwall and/or over the airfoil. For example, the endwallcan have a trough proximate a pressure sidewall of the airfoil and/or abump proximate a leading edge of the airfoil on one or more of apressure side or a suction side of the leading edge. In addition, theairfoil can have a profile that can enhance fluid flow over the airfoiland/or over the endwall. The profiles of the endwall and/or the airfoilcan be defined using multiple sets of two-dimensional coordinates, eachset being provided for a respective section of the respective profilealong the axial direction of the endwall and/or the span of the airfoil.The profile can be used to determine and/or design a throat of a stageincluding the bucket and/or profile to enhance fluid flow from the stageto a next stage or other portion of a turbine in which the bucket isemployed. The contour and/or the profile can take into account coolantor cooling passages in the base and/or airfoil, which passages caninclude an improved tipturn that can reduce stresses in the airfoil andbucket as a whole.

As used herein, the terms “axial” and/or “axially” refer to the relativeposition/direction of objects along axis A, which is substantiallyparallel to the axis of rotation of the turbomachine (in particular, therotor section). As further used herein, the terms “radial” and/or“radially” refer to the relative position/direction of objects along anyradius r extending substantially perpendicular to a rotational orlongitudinal axis A, also called an axis of rotation. Additionally, theterms “circumferential” and/or “circumferentially” refer to the relativeposition/direction of objects along a circumference which surrounds axisA but does not intersect axis A at any location. A Cartesian coordinatesystem used to define the shape of the airfoil and/or endwall contour isdefined further herein, and may operate independently from the axial,radial, etc., directional indicators.

Referring to the drawings, FIG. 1 shows a perspective partial cut-awayillustration of a turbine 10, such as a gas or steam turbine. Turbine 10can include a rotor 12 that with a rotating shaft 14 and a plurality ofaxially spaced rotor wheels 18. A plurality of dynamic blades or buckets20 can be mechanically coupled to each rotor wheel 18, and can bearranged in a row that can extend circumferentially around a respectiverotor wheel 18. So arranged, when a rotor wheel 18 rotates, itsrespective dynamic blades or buckets 20 can revolve about an axis ofrotation of the respective rotor wheel. A nozzle 21 can support aplurality of stationary blades or nozzles 22 circumferentially aroundshaft 14 between adjacent rotor wheels 18 and/or rows of dynamic buckets20. Blades or nozzles 22 can cooperate with dynamic blades or buckets 20to form a stage of turbine 10 and to define a portion of a flow paththrough turbine 10. As shown, nozzle 21 can at least partially surroundrotor 12 (shown in this cut-away view) and in embodiments can completelysurround rotor 12.

While turbine 10 is shown in FIG. 1 as a dual-flow turbine 10 with anaxially centered inlet mouth feeding two sets of turbine stages, variousteachings disclosed herein can be applied to any suitable turbine, suchas an axial turbine with a single primary direction of flow. Forexample, various teachings herein can be applied to an axial inlet gasturbine in which a combustion gas passes through an inlet at a firstaxial end, any stages of the turbine, and an outlet at a second axialend of the turbine, which enables the gas to performed mechanic work onthe turbine.

In operation of the example turbine 10 shown in FIG. 1, gas 24 can enteran inlet 26 of turbine 10 and can flow and/or be directed throughstationary blades or nozzles 22. Stationary blades or nozzles 22 candirect gas 24 against dynamic blades or buckets 20 so that gas 24 canpass around and/or over dynamic blades or buckets 20. As a result ofaerodynamic interaction between dynamic blades or buckets 20 and gas 24,dynamic blades or buckets 20 can impart rotation to rotor wheel 18. Inembodiments of the invention disclosed herein, turbine 10 can includemultiple stages, which can each include a respective row of stationaryblades or nozzles 22 in nozzle 21 and a respective row of dynamic bladesor buckets 20 on a respective rotor wheel 18. It should be understoodthat, while there may be a plurality of rotor wheels 18, they can all beaffixed to shaft 14 so as to rotate in unison, all dynamic blades orbuckets 20 thus imparting rotation on shaft 14 in concert.

In the example shown in FIG. 1, turbine 10 can include five stagesidentified as a first stage L4, a second stage L3, a third stage L2, afourth stage L1, and a fifth stage L0, which is also the last stage.Each stage has a respective radius, with first stage L4 having thesmallest radius of the five stages and each subsequent stage having alarger radius, with fifth stage L0 having a largest radius of the fivestages. While five stages are shown in FIG. 1, this simply anon-limiting example, and the teachings herein can be applied toturbines having more or fewer stages, including a turbine with a singlestage. In addition, while the example shown in FIG. 1 is stationary, theteachings herein can be applied to any suitable turbine, includingturbines used in aircraft engines, and may also be applied tocompressors.

Each set of blades 20, 22 has a number of factors that can affectperformance of turbine 10. For example, FIGS. 2 and 3 illustrate part ofa set of circumferentially spaced-apart blades 200, which will bedescribed as dynamic blades or buckets 20 of a rotor wheel 18, thoughaspects of the description can apply to sets of stationary blades ornozzles 22 depending on a particular implementation. Additionalreference can be made to FIG. 4, which shows a single bucket 200 ofembodiments in perspective. It is understood that bucket 200 can beconfigured to couple (mechanically couple via fasteners, welds,slot/grooves, contact, etc.) with a plurality of similar and/or distinctbuckets (e.g., buckets 200 or other buckets) to form a set of buckets ina stage of the turbine. In addition, bucket 200 can be attached to arotor wheel to form a set of buckets, which rotor wheel can be mountedon a shaft with fasteners, slots and grooves, welds, and/or otherdevices and/or techniques, and/or a hub of the rotor wheel can beintegral with the shaft, and/or the hub can include a portion of theshaft that can be attached to other portions of the shaft via anysuitable coupling.

Each bucket 200 can include an airfoil 202 with a pressure sidewall 204and an opposed suction sidewall 206, as well as a leading edge 208 and atrailing edge 210. Each airfoil 202 can include a chord C betweenleading edge 208 and trailing edge 210 such that pressure and suctionsidewalls 204, 206 can be said to extend in chord or chordwise betweenleading edge 208 and trailing edge 210. Airfoil 202 can be supported bya base 212, and a fillet 214 can connect a first end 215, such as aroot, of airfoil 202 to a first endwall 216, such as a radially innerendwall. Fillet 214 can include a weld or braze fillet, which can beformed via conventional MIG welding, TIG welding, brazing, etc., and caninclude a profile that can reduce fluid dynamic losses as a result ofthe presence of fillet 214. In embodiments, base 212, airfoil 202, andfillet 214 can be formed as a single component, such as by castingand/or machining and/or 3D printing and/or any other suitable techniquenow known or later developed and/or discovered.

As is known in the art, base 212 can be designed to fit into a matingslot in a hub of a rotor wheel and/or a turbine rotor shaft, such asshaft 14 of FIG. 1, and can engage and/or mate with adjacent basecomponents of other buckets 200 if desired and/or suitable. In the caseof a stationary blade or nozzle, base 212 can be designed to fit into aslot or other mounting feature in a nozzle of a turbine, such as nozzle21 of FIG. 1. In embodiments, because base 212 of dynamic blade orbucket 200 can have a relatively large mass, base 212 can be designed tobe located radially inboard of airfoil 202 to reduce forces and stressesarising from revolution of bucket 200 about an axis of rotation duringrotation of a respective rotor wheel and/or turbine shaft. Shouldappropriate materials and/or techniques be developed, base 212 and/orendwall 216 could instead be designed to be radially outward of airfoil202. In addition, in embodiments in the case of a stationary blade ornozzle, the corresponding base can be radially outward of thecorresponding airfoil.

Airfoil 202 of dynamic blade or bucket 200 can extend radially fromendwall 216 and can further have a span S between first end 215 and asecond end 217, such as a tip, of airfoil 202. Pressure and suctionsidewalls 204, 206 can be said to extend in span or spanwise betweenfirst and second ends 215, 217 of airfoil 202. That is, each bucket 200can include an airfoil 202 having opposed pressure and suction sidewalls204, 206 extending in chord or chordwise between opposed leading andtrailing edges 208, 210 and extending in span or spanwise betweenopposed first and second ends 215, 217 of airfoil 202.

First endwall 216 can include a first contour 218 in embodiments, aswill be described below, to alter flow patterns in a passage 219 formedbetween each pair of airfoils 202 and endwall 216. First contour 218 caninclude features, such as bumps and troughs, that can be describedrelative to a nominal surface N of endwall 216. Nominal surface N neednot be an actual, physical surface, and instead can simply be a frame ofreference. While any surface can be employed, in embodiments,referential or nominal surface N can be substantially cylindrical andlocated at any suitable known location. For example, nominal surface Ncan be located at a known radius of curvature, such as a radial distancefrom an axis of rotation of turbine 10 and/or where a surface of anuncontoured endwall ordinarily would be.

With particular reference to FIG. 3, each passage 219 between each pairof airfoils 202 can be regarded as bounded by pressure sidewall 204 of afirst airfoil 202, suction sidewall 206 of a second airfoil 202, andportions of first endwall 216 of each of the first and second buckets200. In FIG. 3, contour lines or isoclines are used to represent a shapeof first contour 218 and relative heights and/or elevations of featuresthereof, each line representing a particular height and/or elevation ofa surface of endwall 216. To illustrate, a nominal contour in FIG. 3 hasbeen labeled “N,” and each other contour has been labeled according tohow far it deviates from nominal, positive and negative. In embodiments,second end 217 of each airfoil 202 can end proximate to a second endwall221, such as a radially outer endwall or shroud, and portions ofadjacent second endwalls 221 can act as an additional boundary ofpassage 219. Where airfoil 202 is part of a stationary blade or nozzle,second end 217 can be connected to second endwall 221. In either case,connected or not, second endwall 221 can include a second contour, whichcan be the same as first contour 218 of first endwall 216, though inembodiments can differ from first contour 218, particularly since flowat second endwall 221 can differ significantly from flow at firstendwall 216.

A set of coordinates can be used to describe and/or define athree-dimensional profile of each airfoil. For example, a unique set orloci of points in space can be provided, such as those listed in TABLEI, below, and can meet stage requirements for manufacture andperformance. The loci of points can be arrived at by iteration betweenaerodynamic, thermal, and mechanical loadings enabling operation in anefficient, safe, and smooth manner. The loci, as embodied by theinvention, can define the bucket airfoil profile for airfoil 202 and cancomprise a set of points relative to any suitable frame of referenceand/or origin, such as the axis of rotation of turbine 10, a coordinatesystem of turbine 10, and/or an origin located at a desired and/orsuitable point of the airfoil and/or base and/or any other suitablecomponent.

For example, a Cartesian coordinate system of X, Y, and Z values can beused to define a profile of airfoil 202, such as the values listed inTABLE I, below. With the origin at leading edge 208 at first end or root215, such as at and/or in nominal surface N, the X and Y axes can berotated such that the X axis extends along a chord of airfoil 202 at thenominal surface N, and such that the Y axis lies orthogonal to the Xaxis in the nominal surface N. The Z axis can then extend radially awayfrom nominal surface N. Any other suitable orientation of the axesrelative to airfoil 202 can be used so long as such orientation is takeninto account in the resulting coordinate values. In embodiments, thecoordinate system that defines the profile can be based on its owngeometry and thus can be used to produce an airfoil with the describedprofile regardless of its location.

With reference to FIG. 2, a plurality of locations 270-278 along span S,including at root 215 and tip 217, can correspond to Z coordinate valuesof chord lines, and a cross section of airfoil 202 at each location canbe described by a respective set of X and Y coordinates. For example,100 points can be listed for each of pressure side 204 and suction side206 for each cross section 270-278, though it should be apparent thatmore or fewer points can be used for each cross section, and more orfewer cross sections can be used, as may be desired and/or appropriate.In the particular set of values shown in TABLE I, eleven sections arerepresented including at first end or root 215, such as in nominalsurface N, and second end or tip 217, intervening sections beingsubstantially evenly distributed therebetween, as should be apparentfrom a review of the Z coordinate values. An origin, therefore, can belocated at a leading edge root of airfoil 202, as illustrated by theaxes in FIG. 4. Further, as suggested above, 200 points are listed foreach cross section, 100 for pressure side 204 and 100 for suction side206, for a total of 2,200 points or sets of coordinate values. The X, Y,and Z coordinate values in TABLE I have been expressed innon-dimensionalized form representing normalized distances in valuesthat can range from −1 to 1, but it should be apparent that any or allof the coordinate values could instead be expressed in distance units solong as the proportions are maintained. TABLE I includes the heading,“Non-Dimensionalized (X Y Z/Span),” and in embodiments a desired spancan be used to convert a coordinate value of TABLE I to a respectivecoordinate value in units of distance, such as inches or meters. Inother words, the non-dimensional values given in TABLE I can bemultiplied by a desired span of airfoil 202, such as, for example, adesired span of between about 7 inches and about 15 inches, such asbetween about 10 inches and about 12 inches, to obtain coordinate valuesin units of distance. By connecting the X and Y values with smoothcontinuing arcs, each profile cross section at each distance Z can befixed, and the airfoil profiles of the various surface locations betweenthe distances Z can be determined by smoothly connecting adjacentprofile sections to one another, thus forming the airfoil profile.

The 2,200 points for the coordinate values shown in TABLE I aregenerated and shown to five decimal places for determining the profileof a nominal airfoil 202 at ambient, non-operating, or non-hotconditions, and do not take any coatings or fillets into account, thoughembodiments could account for other conditions, coatings, and/orfillets. To allow for typical manufacturing tolerances and/or coatingthicknesses, ±values can be added to the values listed in TABLE I,particularly to the X and Y values therein. For example, a tolerance ofabout 10-20 percent of a thickness of the trailing edge in a directionnormal to any surface location along the airfoil profile can define anairfoil profile envelope for a bucket airfoil design at cold or roomtemperature. In other words, a distance of about ±10% to about ±20%(±0.010 to ±0.020 non-dimensionally) of the thickness of the trailingedge in a direction normal to any surface location along the airfoilprofile can define a range of variation between measured points on anactual airfoil surface and ideal positions of those points, particularlyat a cold or room temperature, as embodied by the invention. The bucketairfoil design, as embodied by the invention, is robust to this range ofvariation without impairment of mechanical and aerodynamic functions.Likewise, the profile and/or design can be scaled up or down, such asgeometrically, without impairment of operation, such as by using alarger or smaller desired span.

As mentioned above, endwall contours can affect flow through passage219. A set of coordinate values can be provided, either separately or,particularly where airfoil 202 and base 212 are formed as one piece,along with coordinate values describing a profile of airfoil 202 todescribe and/or define endwall contour 218, should such be desiredand/or appropriate. The same can be done for a contour of second endwall217, if present. Conventional buckets typically employ substantiallyaxisymmetric and/or substantially cylindrical endwall contours. However,base 212 of turbine bucket 200 can have an endwall 216 with anon-axisymmetric contour 218 in embodiments. Using a non-axisymmetriccontour 218 can improve flow around airfoil 202 and through each passage219 of a turbine stage, which can allow for increased firingtemperatures, increased efficiency, and reduced emission of combustionproducts that might be considered undesirable, such as oxides ofnitrogen.

As can be seen in FIGS. 3 and 4, recalling that FIG. 3 employs contourlines to represent relative height and/or elevation of a surface ofendwall 216, contour 218 of endwall 216 can extend along base 212 in acircumferential direction and/or a longitudinal direction, a radialdistance to a surface of endwall 216 varying within contour 218. Base212 can include opposed endwall leading and trailing edges 240, 242 thatcan be at and/or upstream of airfoil leading edge 208 and at and/ordownstream of airfoil trailing edge 210, respectively. Endwall leadingand trailing edges 240, 242 can be opposed, for example, in an axial orlongitudinal direction. In addition, base 212 can includecircumferentially opposed endwall pressure and suction splitlines 244,246. It can also be useful to refer to endwall leading and trailing edgeregions 248, 250 extending from endwall leading and trailing edges 240,242, respectively, toward each other in a longitudinal direction and toabout halfway therebetween. Further, airfoil 202 can be construed asdividing endwall 216 into pressure and suction side regions 252, 254extending from pressure and suction sidewalls 204, 206 toward edges 240,242, 244, 246 of endwall 216. A pitch between centerlines of twoairfoils 202 mounted adjacent one another can be substantially equal toabout a distance between pressure and suction splitlines 244, 246.

To describe and/or define contour 218, nominal surface N can be used,and a relative distance perpendicular to nominal surface N can bedescribed, or can be provided as coordinates, if so desired, for aseries of points along referential surface N. For example, points oflarger radius than nominal surface N can be described as positive, andpoints of smaller radius than nominal surface N can be described asnegative. A specific region of change in position and/or radius of thesurface of endwall 216 relative to nominal surface N can be called afeature. A feature including primarily positive points can be called anelevation or a bump, and a feature including primarily negative pointscan be called a recess or a trough. Normalized coordinate values couldbe used to describe contour 218 in embodiments, such as by using anormalized change in elevation and/or radius relative to nominal surfaceN as a Z coordinate in a Cartesian coordinate system similar to thatused to describe the profile of airfoil 202. For example, a differencefrom nominal surface N could be normalized with a radius of nominalsurface N. X and Y coordinates could then be used to identify thelocation of the difference in nominal surface N. Alternatively, as inthe instant disclosure, specific features of endwall contour 218 can bedescribed relative to dimensions of airfoil 202, endwall 216, and/orbucket 200 as a whole.

In embodiments, contour 218 can include at least one feature in pressureside region 252, suction side region 254, leading edge region 248,and/or trailing edge region 250. Any such feature can include a bump ora trough as may be suitable and/or desired, particularly as may enhanceefficiency, reduce fluid dynamic losses, and/or enhance strength and/oruseful life of bucket 200 and/or turbine 10 (FIG. 1). It should berecognized that fillet 214 can be modified to accommodate endwallcontour 218 and to reduce fluid dynamic and other losses.

For example, with reference to FIGS. 3 and 4, contour 218 can include afirst bump 258 in pressure side region 252, such as on a pressure sideof airfoil leading edge 208, as well as a second bump 260 in pressureside region 252, such as at about midchord in pressure side region 252,though embodiments can include only one of first or second bumps 258,260, as may be desired and/or suitable. In embodiments, first bump 258can extend along and from pressure sidewall 204 from about leading edge208 to about an eighth of the way between leading and trailing edges208, 210. For example, first bump 258 can have a peak at from about 5%chord to about 10% chord in pressure side region 252 and from about 0%to about 5% of pitch away from pressure sidewall 204. In embodiments,first and/or second bump 258, 260 can have a highest relative elevationof from about 3·10⁻² to about 9·10⁻² times a height of bucket 200 abovenominal. Thus, for a bucket 14 inches high, a highest point of firsttrough 262 can be from about 0.42 inches to about 1.26 inches abovenominal. As another example, second bump 260 can have a peak at fromabout 35% chord to about 55% chord in pressure side region 252 and fromabout 10% to about 30% of pitch away from pressure sidewall 204. Thus,contour 218 can include at least one pressure side feature, which caninclude first bump 258 and/or second bump 260. As seen from pressuresplitline 244, therefore, and progressing from endwall leading edge 240to endwall trailing edge 242, endwall 216 in pressure side region 252can rise into first bump 258, descend to a lower level, rise into secondbump 260, and then descend into substantially nominal surface N,particularly along pressure sidewall 204. This is illustrated with theassistance of contour lines and profiles of sections taken along linesA-A, B-B, C-C, and D-D in FIG. 3.

Contour 218 can also include a first trough 262 in suction side region254, that can extend, for example, from a suction side of airfoilleading edge 208 along suction sidewall 206 to about midchord and/orinto suction side region 254. In embodiments, first trough 262 can havea lowest elevation relative to nominal surface N at from about oneeighth to about half of the distance between leading edge 240 andtrailing edge 242 of base 212, such as proximate and/or at suctionsidewall 206 and/or extending into suction side region 254. For example,first trough 262 can have a lowest point at from about 15% chord toabout 20% chord from leading edge 208 and at from about 0% to about 10%pitch from suction sidewall 206. In embodiments, a lowest point of firsttrough 262 can be from about 2·10⁻³ to about 7·10⁻³ times a height ofbucket 200 below nominal. Thus, for a bucket 14 inches high, a lowestpoint of first trough 262 can be from about 0.028 inches to about 0.098inches below nominal. Endwall 216 in suction side region 254, therefore,as viewed from suction splitline 246 and progressing from endwallleading edge 240 to endwall trailing edge 242, can descend fromsubstantially nominal surface N at endwall leading edge 240 into firsttrough 262, then rise into substantially nominal surface N in trailingedge region 250, particularly proximate suction sidewall 206. This isillustrated with the assistance of contour lines and profiles ofsections taken along lines A-A, B-B, C-C, and D-D in FIG. 3.

In embodiments, endwall contour 218 can include a bullnose profile 263of endwall leading edge 240. For example, endwall contour 218 candescend from at least one of second bump 260, first trough 262, ornominal surface N to a lip 265. Lip 265 in embodiments can have a curvedprofile, such as a semi-cylindrical profile, as viewed along thecircumferential direction. Since endwall contour 218 varies alongendwall leading edge 240, bullnose profile 263 can also vary, though lip265 can be substantially consistent. Using such a bullnose profile 263in embodiments can further enhance flow over endwall 216 and/or airfoil202 and/or through flow passage 219. This is illustrated with theassistance of contour lines and profiles of sections taken along linesA-A, B-B, C-C, and D-D in FIG. 3.

Turning to FIG. 5, a schematic view of portions of a multi-shaftcombined cycle power plant 900 is shown. Combined cycle power plant 900may include, for example, a gas turbine 980 operably connected to agenerator 970. Generator 970 and gas turbine 980 may be mechanicallycoupled by a shaft 915, which may transfer energy between a drive shaft(not shown) of gas turbine 980 and generator 970. Also shown in FIG. 5is a heat exchanger 986 operably connected to gas turbine 980 and asteam turbine 992. Heat exchanger 986 may be fluidly connected to bothgas turbine 980 and a steam turbine 992 via conventional conduits(numbering omitted). Gas turbine 980 and/or steam turbine 992 mayinclude one or more buckets 200 as shown and described with reference toFIGS. 2-4 and/or other embodiments described herein. Heat exchanger 986may be a conventional heat recovery steam generator (HRSG), such asthose used in conventional combined cycle power systems. As is known inthe art of power generation, HRSG 986 may use hot exhaust from gasturbine 980, combined with a water supply, to create steam which is fedto steam turbine 992. Steam turbine 992 may optionally be coupled to asecond generator system 970 (via a second shaft 915). It is understoodthat generators 970 and shafts 915 may be of any size or type known inthe art and may differ depending upon their application or the system towhich they are connected. Common numbering of the generators and shaftsis for clarity and does not necessarily suggest these generators orshafts are identical. In another embodiment, shown in FIG. 6, a singleshaft combined cycle power plant 990 may include a single generator 970coupled to both gas turbine 980 and steam turbine 992 via a single shaft915. Steam turbine 992 and/or gas turbine 980 may include one or morebuckets 200 shown and described with reference to FIGS. 2-4 and/or otherembodiments described herein.

The apparatus and devices of the present disclosure are not limited toany one particular engine, turbine, jet engine, generator, powergeneration system or other system, and may be used with other aircraftsystems, power generation systems and/or systems (e.g., combined cycle,simple cycle, nuclear reactor, etc.). Additionally, the apparatus of thepresent invention may be used with other systems not described hereinthat may benefit from the increased reduced tip leakage and increasedefficiency of the apparatus and devices described herein.

TABLE I Non-Dimensionalized (X Y Z/Span) N Location X Y Z 1 suction-side−0.01216 0.02917 0.00000 2 suction-side −0.01146 0.04003 0.00000 3suction-side −0.01108 0.01829 0.00000 4 suction-side −0.00946 0.050730.00000 5 suction-side −0.00727 0.00810 0.00000 6 suction-side −0.006520.06124 0.00000 7 suction-side −0.00289 0.07150 0.00000 8 suction-side0.00000 0.00000 0.00000 9 suction-side 0.00132 0.08149 0.00000 10suction-side 0.00602 0.09124 0.00000 11 suction-side 0.01110 0.100760.00000 12 suction-side 0.01655 0.11009 0.00000 13 suction-side 0.022340.11924 0.00000 14 suction-side 0.02844 0.12820 0.00000 15 suction-side0.03480 0.13694 0.00000 16 suction-side 0.04142 0.14550 0.00000 17suction-side 0.04828 0.15383 0.00000 18 suction-side 0.05535 0.161950.00000 19 suction-side 0.06261 0.16987 0.00000 20 suction-side 0.070080.17756 0.00000 21 suction-side 0.07776 0.18506 0.00000 22 suction-side0.08563 0.19235 0.00000 23 suction-side 0.09373 0.19943 0.00000 24suction-side 0.10203 0.20629 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0.06241 0.19694 0.10000 21suction-side 0.06992 0.20509 0.10000 22 suction-side 0.07772 0.212980.10000 23 suction-side 0.08577 0.22063 0.10000 24 suction-side 0.094100.22804 0.10000 25 suction-side 0.10273 0.23518 0.10000 26 suction-side0.11160 0.24200 0.10000 27 suction-side 0.12071 0.24849 0.10000 28suction-side 0.13004 0.25462 0.10000 29 suction-side 0.13961 0.260350.10000 30 suction-side 0.14941 0.26568 0.10000 31 suction-side 0.159430.27057 0.10000 32 suction-side 0.16971 0.27502 0.10000 33 suction-side0.18022 0.27900 0.10000 34 suction-side 0.19090 0.28242 0.10000 35suction-side 0.20170 0.28526 0.10000 36 suction-side 0.21262 0.287510.10000 37 suction-side 0.22365 0.28914 0.10000 38 suction-side 0.234830.29011 0.10000 39 suction-side 0.24606 0.29041 0.10000 40 suction-side0.25728 0.29004 0.10000 41 suction-side 0.26836 0.28896 0.10000 42suction-side 0.27933 0.28718 0.10000 43 suction-side 0.29018 0.284730.10000 44 suction-side 0.30095 0.28158 0.10000 45 suction-side 0.311530.27779 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The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the disclosure.As used herein, the singular forms “a”, “an” and “the” are intended toinclude the plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising,” when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal languages of the claims.

What is claimed is:
 1. A turbomachine bucket comprising: a base; anairfoil supported by the base, the airfoil including opposed first andsecond ends with the first end at the base, the airfoil furtherincluding opposed pressure and suction sidewalls extending in chordbetween opposed leading and trailing edges and extending in span betweenthe first and second ends of the airfoil; an endwall on the base andconnected to the first end of the airfoil, the endwall including opposedendwall leading and trailing edges extending substantiallycircumferentially between opposed pressure and suction splitlines, adistance between the pressure and suction splitlines being substantiallyequal to a pitch; opposed leading edge and trailing edge regions of theendwall each extending from the respective endwall leading and trailingedges to about half way therebetween; pressure side and suction sideregions of the endwall extending from the respective pressure andsuction sidewalls of the airfoil; at least one pressure side feature inthe endwall in the pressure side region, each respective pressure sidefeature including at least one of a trough or a bump relative to anominal surface of the endwall, wherein the at least one pressure sidefeature includes a first bump in the leading edge region, a second bumpbetween the first bump and the trailing edge of the airfoil, and fromthe endwall leading edge to the endwall trailing edge, the pressure sideregion of the endwall rises into the first bump, descends to a lowerlevel, rises into the second bump, then descends into substantially thenominal surface; at least one suction side feature in the endwall in thesuction side region, each respective suction side feature including atleast one of a trough or a bump relative to the nominal surface of theendwall; and at least one leading edge feature in the endwall includingat least one of a trough or a bump relative to the nominal surface inthe leading edge region.
 2. The turbomachine bucket of claim 1, whereinat least one of the suction sidewall or the pressure sidewall includes anominal profile substantially in accordance with non-dimensionalCartesian coordinate values of X, Y, and Z set forth in TABLE I, whereinthe coordinate values are non-dimensionalized and convertible todistances by multiplying the coordinate values by a desired span inunits of distance, and wherein X and Y values connected by smoothcontinuing arcs define profile sections of the at least one of thesuction sidewall or the pressure sidewall at each distance Z along theairfoil, the profile sections at the Z distances being joined smoothlywith one another to form the profile of the at least one of the suctionsidewall or the pressure sidewall.
 3. The turbomachine bucket of claim1, wherein the first bump has a peak at from about 5% chord to about 10%chord in the pressure side region and from about 0% to about 5% of pitchaway from the pressure sidewall.
 4. The turbomachine bucket of claim 1,wherein the second bump has a peak at from about 35% chord to about 55%chord in the pressure side region and from about 10% to about 30% ofpitch away from the pressure sidewall.
 5. The turbomachine bucket ofclaim 1, wherein the at least one suction side feature includes atrough.
 6. The turbomachine bucket of claim 5, wherein the trough has alowest point at from about 15% chord to about 20% chord from the airfoilleading edge and at from about the suction sidewall to about 10% ofpitch away from the suction sidewall.
 7. The turbomachine bucket ofclaim 1, wherein the at least one pressure side feature includes a bumpin the leading edge region and substantially extending from the leadingedge of the airfoil toward the pressure splitline, a trough in theleading edge region substantially extending from the leading edge of theairfoil toward the suction splitline, and the endwall, and from thepressure splitline to the suction splitline, the leading edge regionrises into the first bump, descends into the trough, and rises tosubstantially the nominal surface.
 8. The turbomachine bucket of claim1, wherein the endwall leading edge includes a bullnose profile thatdescends from at least one of the at least one pressure side feature,the at least one suction side feature, or the nominal surface to asubstantially semi-cylindrical lip below the nominal surface.
 9. Anendwall of a flow passage formed by adjacent first and secondsubstantially identical, substantially circumferentially spaced apartairfoils of adjacent buckets of a stage of a turbomachine, a spacingbetween adjacent airfoils being a pitch, each airfoil includingrespective opposed pressure and suction sidewalls extending chordwisebetween opposed leading and trailing edges and extending spanwisebetween opposed first and second ends, at least one of the suctionsidewall or the pressure sidewall of at least one airfoil including anominal profile substantially in accordance with non-dimensionalCartesian coordinate values of X, Y, and Z set forth in TABLE I, whereinthe coordinate values are non-dimensionalized and convertible todistances by multiplying the coordinate values by a desired span inunits of distance, and wherein X and Y values connected by smoothcontinuing arcs define profile sections of the at least one of thesuction sidewall or the pressure sidewall at each distance Z along theairfoil, the profile sections at the Z distances being joined smoothlywith one another to form the profile of the at least one of the suctionsidewall or the pressure sidewall, the endwall comprising: a nominalsurface between opposed endwall leading and trailing edges and includinga region between the pressure sidewall of the first airfoil and thesuction sidewall of the second airfoil; at least one pressure sidefeature including at least one bump relative to the nominal surfaceproximate the pressure sidewall of the first blade; and at least onesuction side feature including at least one trough relative to thenominal surface.
 10. The endwall of claim 9, wherein the at least onebump incudes a first bump proximate the leading edge of the firstairfoil.
 11. The endwall of claim 10, wherein the first bump has a peakat from about 5% chord to about 10% chord from the leading edge and fromabout 0% to about 5% of pitch from the pressure sidewall.
 12. Theendwall of claim 9, wherein the at least one bump includes a first bumplocated adjacent and at about midchord of the pressure sidewall of thefirst airfoil.
 13. The endwall of claim 12, wherein the first bump has apeak at from about 35% chord to about 55% chord away from the leadingedge and from about 10% to about 30% of pitch from the pressuresidewall.
 14. The endwall of claim 9, wherein the at least one troughincludes a first trough proximate the leading edge of the secondairfoil.
 15. The endwall of claim 14, wherein the first trough has alowest point at from about 15% chord to about 20% chord from the leadingedge and from about 0% to about 10% of pitch away from the suctionsidewall.
 16. A turbine system comprising: a compressor section; acombustion section; a turbine section including at least one stage ofairfoils substantially circumferentially distributed at a pitch about anaxis of rotation of the turbine section, each airfoil supported by arespective platform of a respective bucket such that adjacent airfoilsform a flow passage including a pressure sidewall of a first airfoil, asuction sidewall of a second, adjacent airfoil, and an endwall formed byat least a portion of each of the respective platforms of the first andsecond airfoils, at least one of the suction sidewall or the pressuresidewall including a nominal profile substantially in accordance withnon-dimensional Cartesian coordinate values of X, Y, and Z set forth inTABLE I, wherein the coordinate values are non-dimensionalized andconvertible to distances by multiplying the coordinate values by adesired span in units of distance, and wherein X and Y values connectedby smooth continuing arcs define profile sections of the at least one ofthe suction sidewall or the pressure sidewall at each distance Z alongthe airfoil, the profile sections at the Z distances being joinedsmoothly with one another to form the profile of the at least one of thesuction sidewall or the pressure sidewall.
 17. The turbine system ofclaim 16, wherein the endwall includes at least one bump proximate thepressure sidewall of the first airfoil and at least one trough proximatethe suction side of the second airfoil.
 18. The turbine system of claim16, wherein the at least one bump includes a first bump proximate theleading edge of the first airfoil with a peak at from about 5% chord toabout 10% chord from the leading edge and from about 0% to about 5% ofpitch away from the pressure sidewall, and a second bump proximate amidchord of the second airfoil with a peak at from about 35% chord toabout 55% chord away from the leading edge and from about 10% to about30% of pitch away from the pressure sidewall, and the at least onetrough includes a first trough with a lowest point at from about 15%chord to about 20% chord from the leading edge and from about 0% toabout 10% of pitch away from the suction sidewall.
 19. The turbinesystem of claim 16, wherein for each airfoil both a respective suctionsidewall and a respective pressure sidewall include a nominal profilesubstantially in accordance with non-dimensional Cartesian coordinatevalues of X, Y, and Z set forth in TABLE I, wherein the coordinatevalues are non-dimensionalized and convertible to distances bymultiplying by a desired span in units of distance, and wherein X and Yvalues connected by smooth continuing arcs define airfoil profilesections at each distance Z along the airfoil, the profile sections atthe Z distances being joined smoothly with one another to form theairfoil profile.
 20. A turbomachine bucket comprising: a base; anairfoil supported by the base, the airfoil including opposed first andsecond ends with the first end at the base, the airfoil furtherincluding opposed pressure and suction sidewalls extending in chordbetween opposed leading and trailing edges and extending in span betweenthe first and second ends of the airfoil; an endwall on the base andconnected to the first end of the airfoil, the endwall including opposedendwall leading and trailing edges extending substantiallycircumferentially between opposed pressure and suction splitlines, adistance between the pressure and suction splitlines being substantiallyequal to a pitch; opposed leading edge and trailing edge regions of theendwall each extending from the respective endwall leading and trailingedges to about half way therebetween; pressure side and suction sideregions of the endwall extending from the respective pressure andsuction sidewalls of the airfoil; at least one pressure side feature inthe endwall in the pressure side region, the at least one pressure sidefeature including a first bump in the leading edge region, a second bumpbetween the first bump and the trailing edge of the airfoil, and fromthe endwall leading edge to the endwall trailing edge, the pressure sideregion of the endwall rises into the first bump, descends to a lowerlevel, rises into the second bump, then descends into substantially thenominal surface.
 21. The turbomachine bucket of claim 20, furthercomprising at least one suction side feature in the endwall in thesuction side region, each respective suction side feature including atleast one of a trough or a bump relative to the nominal surface of theendwall.
 22. The turbomachine bucket of claim 20, further comprising atleast one leading edge feature in the endwall including at least one ofa trough or a bump relative to the nominal surface in the leading edgeregion.
 23. The turbomachine bucket of claim 20, wherein the at leastone pressure side feature includes a bump in the leading edge region andsubstantially extending from the leading edge of the airfoil toward thepressure splitline, a trough in the leading edge region substantiallyextending from the leading edge of the airfoil toward the suctionsplitline, and the endwall, and from the pressure splitline to thesuction splitline, the leading edge region rises into the first bump,descends into the trough, and rises to substantially the nominalsurface.